Never, ever look to Urban Dictionary for the definition of anything. They could find a vile sexual double-meaning in a recipe for homemade ice cream. It’s a website for porn addicted frat boys who like a good gang-rape on a Friday night, not normal people.
A “pudding stick” is someone who “stirs things up”, so to speak. An instigator. Boortz was not calling Sarah Palin anything involving anal intercourse. Like him or not, that’s not what Neal does.
As I said I never heard the term and the only place there is any kind of definition is the place you referred. I don’t know much about the guy other than he has guest hosted a few times on shows I listen to. I can give him the benefit of the doubt, but I think he should be careful with the words he chooses to use. He could have called her a rabble rouser or just said that she stirs things up. Or instead of saying anything bad about her, which he did, he could have said nothing.
Or better yet he could actually do some research on her and discover that she has a record of executive leadership that no other candidate in this campaign can come close to.